The method of $a$-contraction with shifts used for long-time behavior toward viscous shock
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916442543226880 |
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| author | Han, Sungho Kang, Moon-Jin Lee, Hobin |
| author_facet | Han, Sungho Kang, Moon-Jin Lee, Hobin |
| contents | We revisit the method of $a$-contraction with shifts used for long-time behavior of barotropic Navier-Stokes flows perturbed from a Riemann shock. For the usage of the method of $a$-contraction with shifts, we do not employ the effective velocity $h$ variable even for higher order estimates. This approach would be important when handling the barotropic Navier-Stokes system with other effects, for example, such as capillary effect and boundary effect. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12875 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The method of $a$-contraction with shifts used for long-time behavior toward viscous shock Han, Sungho Kang, Moon-Jin Lee, Hobin Analysis of PDEs We revisit the method of $a$-contraction with shifts used for long-time behavior of barotropic Navier-Stokes flows perturbed from a Riemann shock. For the usage of the method of $a$-contraction with shifts, we do not employ the effective velocity $h$ variable even for higher order estimates. This approach would be important when handling the barotropic Navier-Stokes system with other effects, for example, such as capillary effect and boundary effect. |
| title | The method of $a$-contraction with shifts used for long-time behavior toward viscous shock |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.12875 |